A fight in a dream is read as inner conflict as much as outer. Dream books ask what the two sides want, since both are usually yours — the wish to stay and the wish to go, duty against desire. Fighting someone you know is traditionally read as tension with them that has not been spoken aloud, while fighting a stranger points to a quality you are wrestling with in yourself. Winning is taken as finding your strength, and being unable to land a blow — a very common detail — as feeling that your efforts have no effect. It can help to notice where in waking life you are holding back an argument.
Does the traditional reading fit your dream, or did it mean something else to you?
My Cosmic Code has a private dream journal. Write a dream down and the app picks out the symbols in it, shows what dream books say about them and, over time, which words recur across your entries. The journal is stored on your device only.